Special classes of snarks. (English) Zbl 1018.05033

Cavicchioli, A.; Murgolo, T. E.; Ruini, B.; Spaggiari, F.

Acta Appl. Math. 76, No. 1, 57-88 (2003).

Summary: We report the most relevant results on the classification, up to isomorphism, of nontrivial simple uncolorable (i.e., the chromatic index equals 4) cubic graphs, called snarks in the literature. Then we study many classes of snarks satisfying certain additional conditions, and investigate the relationships among them. Finally, we discuss connections between the snark family and some significant conjectures of graph theory, and list some problems and open questions which arise naturally in this research.

MSC:

05C15	Coloring of graphs and hypergraphs
05C45	Eulerian and Hamiltonian graphs

Keywords:

simple cubic graphs; chromatic index; girth; cyclic edge-connectivity; snarks; almost-Hamiltonian snarks; hypo-Hamiltonian snarks; critical snarks; irreducible snarks; total colorings; total chromatic number; flows; computer algorithm